Add wetmaps to joined mesh
While  a face of an object can have only one material, a material can use more than one UV Map, so you can add another UV map to the object to map images generated by Dynamic Paint on to the whole road. You've probably done half of this, but I'll go through the whole thing..


In the UV Maps panel of the road object's Data tab, hit '+' to add a new map. Give it a sensible name, and select it to make it active.
In the header of a UV edit window, you'll find the option to select which UV Map you're defining by the current unwrapping/editing session.. it should show the map you've made active. Unwrap the whole road to it. (Whichever way you like, but probably by looking orthogonally straight down at the road in Edit Mode, and U > 'Project from View - Bounds')
In your shader tree, replace the 'Texture Coordinate' node with two 'Input' > 'UV Map' nodes, one for the tiles, one for the road's Dynamic Paint image sequence. (This tree only illustrates the use of 2 maps, it's not meant to recommend how you might use the rain image sequence to affect the material)





In its Output panel, tell Dynamic Paint to use the all-road UV map when baking its image sequence. (Mine's called UV_All)




Then the tiles keep the mapping from before they were made into an array, and the rain falls on the whole road.